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 A134388 A generalized Riordan array related to Hankel and Toeplitz+Hankel transforms. 1
 1, 1, 1, 1, 2, 1, 2, 3, 2, 1, 3, 6, 4, 2, 1, 6, 10, 8, 5, 2, 1, 10, 20, 15, 10, 6, 2, 1, 20, 35, 30, 21, 12, 7, 2, 1, 35, 70, 56, 42, 28, 14, 8, 2, 1, 70, 126, 112, 84, 56, 36, 16, 9, 2, 1, 126, 252, 210, 168, 120, 72, 45, 18, 10, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Corresponds to the Riordan array ((1+2x)/sqrt(1-4x^2),xc(x^2)), c(x) the g.f. of A000108, with the first column replaced by 1,1,1,2,3,6,... with g.f. (1+2x+sqrt(1-4x^2))/(2*sqrt(1-4x^2)). Alternatively it is the array with first column 1,1,1,2,3,6,... and then the Riordan array ((1+2x)c(x)/sqrt(1-4x^2),xc(x^2)) embedded from the (1,1) position (indexing starting at (0,0)). Row sums are 2^n. Images of common sequences under this array have interesting Hankel transforms. For instance, the image of r^n has Hankel transform with g.f. 1/(1+(r^2-1)x^2). LINKS E.L. Basor, T. Erhardt, Some identities for determinants of structured matrices, arXiv:math/0008075v1 EXAMPLE Triangle begins 1, 1, 1, 1, 2, 1, 2, 3, 2, 1, 3, 6, 4, 2, 1, 6, 10, 8, 5, 2, 1, 10, 20, 15, 10, 6, 2, 1, 20, 35, 30, 21, 12, 7, 2, 1, 35, 70, 56, 42, 28, 14, 8, 2, 1, 70, 126, 112, 84, 56, 36, 16, 9, 2, 1, 126, 252, 210, 168, 120, 72, 45, 18, 10, 2, 1 CROSSREFS Sequence in context: A133088 A059982 A187801 * A055095 A048685 A101050 Adjacent sequences:  A134385 A134386 A134387 * A134389 A134390 A134391 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Oct 23 2007 STATUS approved

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Last modified August 4 07:32 EDT 2020. Contains 336201 sequences. (Running on oeis4.)